Data-Driven Improvement of Local Hybrid Functionals: Neural-Network-Based Local Mixing Functions and Power-Series...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Local hybrid functionals (LHs) incorporate exact exchange (EXX) using a local mixing function (LMF).
• Developing accurate LMFs has been challenging due to a lack of physical constraints on valence behavior.
• Existing methods often require calibration functions to address issues like the gauge problem.

Purpose of the Study:

• To develop a data-driven approach for constructing improved local mixing functions (LMFs) for local hybrid functionals (LHs).
• To train a new type of LMF, termed 'n-LMF', using neural networks and meta-GGA features.
• To evaluate the performance of new LH functionals incorporating n-LMFs for various chemical properties.

Main Methods:

• Trained a shallow neural network to create a new local mixing function (n-LMF) with meta-GGA input features.
• Utilized W4-17 atomization energies and BH76 reaction barriers for training.
• Replaced the standard LMF in LH20t with n-LMF to create LH24n-B95, and further refined it to LH24n using an optimized B97c correlation functional, incorporating DFT-D4 dispersion corrections.

Main Results:

• LH24n-B95-D4 achieved a WTMAD-2 value of 3.49 kcal/mol on the GMTKN55 dataset, a significant improvement over LH20t.
• The refined LH24n-D4 functional reached a WTMAD-2 of 3.10 kcal/mol, the lowest reported for a rung 4 functional in self-consistent calculations.
• The new n-LMF and x-LMF functionals effectively suppress the gauge problem in local hybrids without needing calibration functions.

Conclusions:

• The data-driven approach to train n-LMFs offers a flexible and effective way to improve LH functionals.
• LH24n-D4 represents a state-of-the-art functional for general main-group thermochemistry, kinetics, and noncovalent interactions.
• This method allows for deeper understanding through graphical analysis of LMFs while enabling efficient routine calculations.